Available online at ScienceDirect. Procedia Engineering 119 (2015 )

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1 Available online at ScienceDirect Procedia Engineering 119 (2015 ) th Computer Control for Water Industry Conference, CCWI 2015 Determination of optimal location and settings of Pressure Reducing Valves in Water Distribution Networks for minimizing water losses Juan Saldarriaga a *, Camilo Andrés Salcedo a a Universidad de los Andes Water Distribution and Sewer Systems Research Center (CIACUA), Cra 1E # 18A-53, Bogotá, Colombia Abstract The determination of the optimal location and settings of PRV is an operational problem that water utilities must deal with in order to reduce the real losses that are inherent to their water distribution system. In this research, a multi-objective optimization approach was developed to provide an optimal solution for the addressed problem, using the well-known metaheuristic algorithm NSGA-II and including the usage of hydraulic criteria to reduce the solution space, in order to enhance the performance of the procedure. The proposed methodology was tested using two different networks, which differ in their leakage configuration and the hydraulic parameters used for this modeling The The Authors. Published Published by Elsevier by Elsevier Ltd. This Ltd. is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of the Scientific Committee of CCWI Peer-review under responsibility of the Scientific Committee of CCWI 2015 Keywords: Leakages; NSGA-II; Pressure Management; Pressure Reduction Valves; Water Losses 1. Introduction In Water Distribution Systems (WDS), losses are classified into two categories according to the way the water leaves the network: The volume of water that gets lost through leakages and tank overflows is known as real losses, while the apparent losses occurs as a consequence of improper metering and the unauthorized use of the supplied water. Meanwhile, the Non-Revenue Water (NRW) quantifies the water losses and is considered a measurement of the operational efficiency of the water utilities. This index can reach high values, representing excessive economic * Corresponding author. Tel.: address: jsaldarr@uniandes.edu.co The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of the Scientific Committee of CCWI 2015 doi: /j.proeng

2 974 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) losses to water utilities and turning its minimization into a duty through the use of different techniques such as pressure management, improving pumping patterns, or infrastructure rehabilitation. In the pressure management scheme, the addressed problem consist in the determination of the optimal location and settings for a set of valves, in this case pressure reduction valves (PRV), for reducing the over pressures in the system and consequently, minimizing the leakages as a consequence of their pressure-driven behaviour. Historically, different authors have addressed this problem using different types of valves and approaches, beginning with the determination of the optimal setting of control valves in WDS [1] [2], and later incorporating the localization of those accessories in the system using more than one objective in the scope of the solution [3] [4]. Afterwards, the combined approximation was tested using Pressure Reduction Valves instead of control valves [5], leading the application of this technique to the pressure management scheme for reducing leakages in WDS. This paper presents an approach that seeks to determine the optimal location and daily settings of a set of PRVs in order to minimize the economic losses that leakages represent to the water utilities, and the capital costs required for the installation of the valves. The proposed approximation uses hydraulic concepts that outline the potential locations for PRVs according to the performance of those spots in the pressures of the system in order to reduce the search space and increasing the efficiency of the optimization algorithm. Once the potential locations of PRVs are selected, a NSGA-II is executed aided by the hydraulic solver EPANET, obtaining a Pareto Front that represents the relation between the two objectives explained previously. After the near optimal solution is selected based on the water utilities preferences, its hydraulic behaviour is assessed for determining the feasibility of its implementation. The methodology is tested for some water distribution networks varying the size of the systems and the distribution of the leakages showing the advantages of this approach. Nomenclature WDS PRV NRW Water Distribution System Pressure Reducing Valves Non-Revenue Water 2. Methodology The steps explained lately in this section compose the proposed methodology for locating and determining the settings of a set of PRVs in a WDS in an optimal way seeking to minimize the water losses of the system. 2.1 Economic Quantification of Water Losses The operational performance of the water utilities can be measured by the Non-Revenue Water (NRW), which quantifies the water losses, including real and apparent losses, as a percentage of the volume of water supplied to the WDS. In the case of countries in development, the average NRW for 2009 was 49%, with the existence of some critical cases with an index of 90% in certain zones of the country. As this index is particular to each city (even it could be particular to each WDS), it is expected that the quantification of the water losses are also unique for each region, and consequently each water utility. Therefore, in this research there was developed a cost for water losses specifically for the water utility of Bogotá, as an example which includes the calculation of the drinking water tariff for the city, and also the costs involved in the supplying procedure. Finally, the unperceived profit per lost cubic meter of water was estimated in 0.22 USD/m 3, which is comparable with some studies that indicated this value as 0.2 USD/m 3 for Colombia [6].

3 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) Reduction of the Solution Space When the optimization problem related to the location of valves in a WDS is being addressed, every pipe can be considered as a possible location for one of these accessories, leading to the generation of an enormous solution space. However, if the hydraulic behavior of the network is known, a set of pipes can be selected through the application of hydraulic criteria to build a reduced solution space knowing that those conduits have the highest impact over the pressure surface along the system [4]. Within an optimization procedure, many hydraulic executions of the same system must be done in order to maximize the exploration of the solution space. For example, if a water utility requires the installation of five valves in a WDN composed of 100 pipes, a total of ,520 hydraulic executions are needed to explore the solution space [7]. Therefore, if a set of only 50 pipes is obtained as the potential locations for the valves, the new problem requires 2 118,760 hydraulic executions, achieving a reduction of 97.19% in the number of iterations by reducing the size of the solution space in a 50%. Then, the major advantage of this technique is revealed: By lowering the size of the solution space, the required computational times involved in the optimization process are also reduced in a significant percentage. In the presented approach, three hydraulic criteria were tested in order to establish which one of them reduces the solution space in a more efficient way, reaching to better results than the others do. These concepts were Specific Power, measuring the dissipated energy when water flows through a pipe [6], the Pipe Index, measuring the relative importance of the pipes in a WDN in terms of their hydraulic performance [7], and a sectorization criterion that quantifies the hydraulic effect of closing a pipe in the WDN. For the selection of the hydraulic criteria that reduces the solution space and reaches the best results, a theoretical network was used, applying the algorithm that is described in Section 2.3. Based on the results shown in Fig. 1 (a), it can be deduced that Specific Power and Sectorization Criterion are capable of reaching the best solutions for the tested system, but due to the computational complexity of the latter, the chosen criterion to be used in this approach is the Specific Power (1). In this equation Q is the flow, h f is the friction losses and h m is the minor losses. SP Q( h f hm ) (1) a b Fig. 1. (a) Comparison of the performance of the analyzed hydraulic criteria; (b) Comparison of the effect of the reducing percentage over the solutions obtained. Both variables in USD

4 976 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) Besides the determination of an appropriate criterion for reducing the size of the solution space, an adequate magnitude for this diminution must be established in order to avoid an excessive reduction of the solution space, which could result in the removal of important elements (in hydraulic terms) of the space. In addition, it is desirable that the mentioned magnitude also avoids insignificant reductions that would have no effect over the number of required simulations. To establish the mentioned percentage, a theoretical network of 150 pipes was tested using the optimization methodology that is explained further in Section 2.3, reducing the size of the sets of potential locations for valves in a 50% of the original size, and afterwards in a 90%. The obtained results, shown in Fig. 1 (b), are indicating that the difference between the solutions reached for a reduction of 50% and 90% of the original solution space are irrelevant compared to the reduction of computational time they imply. For this reason, it was preferred to lose a few quality in the optimal Pareto Front in order to achieve a set of solutions of similar quality (in terms of its optimality) in a reduced time, validating the reduction of the solution space to the 10% of its original size. Finally, once the solution space have been reduced using the hydraulic criterion of Specific Power with a reduction percentage of 90%, a new set of potential locations for PRVs is formed, leaving the network ready to pass to the next step of the proposed methodology. 2.3 Multi-objective Optimization: NSGA-II In the determination of the optimal location and settings for a set of valves in a WDS, the usage of a multiobjective approach is preferred rather than a single-objective approximation because the first one leads to an entire set of optimal solutions by considering at least two important criteria in the decision process [2, 3, 4, 5]. Therefore, the Non-Sorting Genetic Algorithm II NSGA II was used in this research for solving the addressed optimization problem, because it is a well-known metaheuristic procedure in the scope of the urban water resources for its capabilities in the achievement of optimal solutions [8]. The NSGA-II used in this research was implemented in MATLAB R2013, based on a version that uses Simulated Binary Crossover (SBX) as the crossover operator, and the Polynomial Mutation as the mutation operator [9]. The recommended set of parameters for each operator includes 0.5 as the crossover probability and as the mutation probability [10] Problem Description In the pressure management scheme, the addressed problem consists in the determination of the optimal location and settings for a set of valves (PRV in this case) for reducing the excess of pressures in the system, seeking to minimize the water lost in the system through leakages as a consequence of their pressure-driven behavior. Fig. 2. Relationship between the demand pattern, the pressure within a WDS and the setting of a PRV

5 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) However, due to the relationship between the demand patterns and the behavior of the pressure within the WDS, as shown in Fig. 2, the setting of the PRV installed in the system must reduce significantly the pressure in the lowdemand periods (night-time); while the setting during the high-demand periods (daytime) must be higher in order to supply properly the water demands. The latter behavior can be achieved with a time-of-day control, which can be used assuming that the water utilities have a well-known demand pattern in their cities with a low variation through the time [11]. According to the description of the addressed problem in this research, the set of optimal solutions is composed by the determination of three decision variables: 1) The location of the PRV, which is a discrete variable that represents the pipe where the PRV is going to be installed; 2) The daytime variation of the setting, defined as an increment of ±20% of the initial PRV setting in order to supply the water during the high-demand period; and 3) The night-time variation of the setting, defined as a reduction of ±10% of the daytime setting in order to supply water during the low-demand periods. In terms of the NSGA-II, the representation of a solution, or individual, is shown in Fig. 3 using the decision variables described lately. The length of each individual, or total number of decision variables, will be of 3n where n represents the number of potential location for valves according to the reduction of the solution space Formulation of the Optimization Problem Fig. 3. Representation of the genes of the ith individual In the urban water context, the multi-objective optimization approaches are made up of one objective focused to the minimization of an economic criterion such as the capital costs of improving a system, while the second objective is motivated to improve the hydraulic performance of the network with different scopes such as reducing water losses, minimizing the transient effect of valves closure or reducing the pumping costs inside a WDS [3]. Related to the hydraulic performance criterion, some authors have proposed different objective functions for the addressed optimization problem: to minimize the sum of deviations from the minimum pressure [12] to maximize the coverage of adequate pressures [13], and the most widely used one, to minimize the leakage volumes [5]. In this research, the latter objective was selected as to represent the hydraulic performance of the WDS, including an economic criterion in order to quantify how much money the water utility does not receive as the water is lost as leakages through the system. Therefore, the resulting objective function (2) seeks to minimize the unperceived annual profits the water utility must assume as a result of the real water losses through the WDS, where represents the unperceived profit per lost cubic meter of water, is the pressure along the ith pipe during the time interval t, corresponds to the width of the time interval, and the leakage parameters and. T NN OF1 U p, t 365 (2) NP t 1 i 1 The second objective used in this research is related to the economic consequences of implementing a proposed solution, which in this case, is the installation of a PRV of diameter d. Therefore, the objective function (3) seeks to minimize the PRVs installation costs per year, where and k are the parameters of a potential regression that i i t

6 978 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) represents the increasing capital cost of valves according to its diameter, and stands for the diameter of the ith valve. The used costs are considered annually, given that according to the most Latin-American countries laws, the payback period for investments in this type of infrastructure is 5 years. n v k OF2 C CV d i (3) t 1 Regarding the constraints of the presented optimization problem, three of them were used in the proposed approach: 1) Mass conservation in each junction of the network; 2) Energy conservation at each pipe of the system; and 3) ensure a minimum operative pressure for all the consumption nodes of the network. To accomplish the fulfillment of constraints 1 and 2, the hydraulic solver EPANET [14] was used, while the last constraint was satisfied due to the NSGA-II Execution of the Optimization Tool An optimization tool was developed in MATLAB R2013, which coupled the NSGA-II with EPANET 2.0 through the programmer s toolkit [14] in order to assess the different solutions proposed by the algorithm, developing as many hydraulic executions of the analyzed WDS as the optimization algorithm required. 2.4 Hydraulic Assessment of Leakage Reduction Once a set of solutions have been reached by the NSGA-II, an optimal solution is selected based on the preferences of the decision maker. In this case, there was assumed that both objectives have the same importance, so, the optimal solution of a problem will be found in the point of maximum curvature of the optimal Pareto Front. Finally, the optimal solution was implemented in EPANET 2.0 in order to assess the leakage reduction, determining the quality of the results. 3. Case Studies The proposed methodology was tested using two different case studies: the first of them is the WDS proposed by Jowitt & Xu [1], which is a well-known benchmark in the context of leakage reduction through valve location; while the second one corresponds to a theoretical version of the subsection 8-04 of the WDS in Bogotá, Colombia [15]. These networks represent diverse hydraulic situations, allowing to the achievement of more reliable results.

7 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) a b Fig. 4. (a) Benchmark Network of Jowitt & Xu [1]; (b) Subsection 8-04 of the WDS of Bogotá, Colombia 3.1 Benchmark WDS: Jowitt & Xu [1] The first system to analyze corresponds to a benchmark that has been used widely by the researchers addressing the problem related to the optimal location of valves for minimizing leakages. This system is composed by 3 reservoirs with total heads of m, 54.6 m and 54.5 m respectively, 37 pipes and 25 junctions as shown in Fig. 4(a). The total pipe length is km, ranging its diameter between 152 and 475 mm, and the Hazen-Williams coefficients for roughness between 6 and 140. In terms of water losses, the Jowitt & Xu s network is characterized by having distributed leakages in all its nodes, representing a background leakage model. The emitter s exponent used in this WDS was 1.18, while the leakages coefficients are ranged between and These hydraulic characteristics leaded to an average supplied flow rate of L/s, and a total of water losses of L/s, representing a NRW of 14.44%. This WDS has a known demand pattern for the junctions and the reservoirs, and it was assumed that the highdemand period begins at 6:00 am and ends at 10:00 pm. 3.2 Subsection 8-04 Bogotá, Colombia [15] The second network to analyze corresponds to a subsection of the real WDS of Bogotá, Colombia. This system is composed by 1 reservoir with total head of 49.5 m, 432 pipes and 378 junctions as shown in Fig. 4(b). The total pipe length is km, ranging its diameter between 76.2 and mm, and an absolute roughness between and 0.03 mm, representing PVC and concrete. In terms of water losses, the Subsection 8-04 of Bogotá s WDS is characterized by having concentrated leakages in certain zones of the system. The emitter s exponent used in this WDS was 0.75, while the leakages coefficient was These hydraulic characteristics leaded to an average supplied flow rate of L/s, and a total of water losses of 7.79 L/s, representing a NRW of 16.3%. This WDS has a known demand pattern, and it was assumed that the high-demand period begins at 8:00 am and ends at 6:00 pm.

8 980 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) Results and Discussion After the proposed approach was applied to the networks used as case studies, the results described below were achieved, showing in both cases an optimal Pareto Front, and analyzing the effect of implementing the solution in terms of the pressure of the WDS. 4.1 Benchmark WDS: Jowitt & Xu [1] Due to the size of the network, the reduction of the solution space was of 59% of the original one, leading to a set of potential locations for PRVs of 22 pipes. After applying the NSGA-II, the Pareto Front shown in Fig. 5 was obtained with an optimal solution that consisted in the implementation of two PRVs with the settings shown in Table 1. This solution represented an annual investment of 5, USD and an unperceived profit for water utility of 160, USD. In hydraulic terms, this solution achieved a reduction of water losses of 4.03 L/s, meaning a leakage flowrate of L/s, which in the analyzed period of time represented a new NRW of 12.87%. Table 1. Optimal Location and Settings for PRV According to the Obtained Solution Valve Initial Setting (m) Daytime Setting (m) ]Night-time Setting (m) As it was mentioned before, many authors have used this network as a benchmark for testing their methodologies, whose results are shown in Table 2. Therefore, for validating the results obtained in this research, the final leakage flowrate was compared to the historical values obtained by those researchers, achieving that the solution in this paper was 0.64% higher than the results of [3], which is an acceptable percentage to consider the obtained solution as successful. Table 2. Results achieved by different authors for Jowitt & Xu Network. Authors Fig. 5. Optimal Pareto Front Obtained for the Network Jowitt & Xu Optimal Location of Valves Optimal Settings of Valves Total Leakage flowrate (L/s) Reis, Porto & Chaudhry, % - 31% - 0% Vairavamoorthy & Lumbers, % - 90% - 0% Araujo, Ramos & Coelho, Nicolini & Zovatto, % - 30% - 0% - 63% - 37% Creaco & Pezzinga,

9 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) Ali, % - 29% - 0% Finally, by analyzing the performance of the pressure management, it was noticed that Valve 01 achieved a reduction in pressure of m, which demonstrated the feasibility of applying this solution. However, the pressure s decrease for Valve 36 was lower, which could be attributed to the looped nature of the network. 4.2 Subsection 8-04 Bogotá, Colombia [15] Due to the large size of the network, the reduction of the solution space was carried out to the 10% of the original one, leading to a set of potential locations for PRVs of 44 pipes. After applying the NSGA-II, the Pareto Front shown in Fig. 6 was obtained with an optimal solution that consisted in the implementation of three PRVs with the settings shown in Table 3. This solution represented an annual investment of 2, USD and an unperceived profit for water utility of 48, USD. In hydraulic terms, this solution achieved a reduction of water losses to a leakage flowrate of 7.03 L/s, which in the analyzed period of time represented a new NRW of 14.36%. Table 3. Optimal Location and Settings for PRV According to the Obtained Solution Valve Initial Setting (m) Daytime Setting (m) ]Night-time Setting (m) Fig. 6. Optimal Pareto Front Obtained for the Subsection 8-04 of the WDS of Bogotá, Colombia In order to validate the obtained solution in this WDS, the contour of pressures during the most critical hour was analyzed as shown in Fig. 7. As it is shown in Fig. 7 (a), the most part of the network is operated with a pressure between 18 and 26 m, and only a small zone is operated near to the minimum pressure, it means, 15 m. After the proposed pressure management scheme is applied, as shown in Fig. 7 (b), the portion of the network that operated near the minimum pressure got bigger, and it is noticed that some other zones in the north-eastern region of the system also lower their pressures, representing a lower surface of pressures, and demonstrating the benefits of using the pressure management in the leakage reduction.

10 982 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) a b Fig. 7. (a) Pressure s contour before Pressure Management during the critical hour; (b) Pressure s contour after Pressure Management during the critical hour. Pressure in m As leakages in this WDS were concentrated in certain zones of the network, it was expected that the optimal location of the PRVs were near to those critical points of the system. However, it was demonstrated that in these cases, the valves are going to be located in zones where there are not leakages in order to lower the surface of pressures in all the network, achieving a water losses reduction, and also a properly pressure management in all the system. 5. Conclusions A multi-objective optimization approach was proposed for solving the problem related to the determination of the optimal location and settings for a set of PRVs within a WDS in order to reduce leakages, and consequently the NRW. To accomplish these, there were considered as the first objective the profits that the water utility did not receive as result of the real water losses and as the second objective the capital costs of implementing the required set of PRVs in the network to accomplish the reduction in real losses. This multi-objective scope was selected because it provides an entire set of optimal solutions where water utilities can choose the most appropriate one according to their preferences among the objectives. Meanwhile, the metaheuristic algorithm used in this research was NSGA-II, which is a well-known procedure in the urban water context for its appropriate performance in solving diverse optimization problems. A computational tool was developed, coupling the implemented algorithm in MATLAB with the hydraulic simulator EPANET, demonstrating the capabilities of this synergy in the optimization scope. Furthermore, to enhance the performance of the algorithm, a reduction in the solution space was proposed considering that there is a trade-off between the optimality of a solution and the computational time required to achieve it. As a conclusion of this, it was preferred to lose some optimality in order to reduce the computational times, and as it was demonstrated, the solution space can be reduced even until a 10% of its original size, making the algorithm to focus only in the most important pipes of the network in hydraulic terms. When the methodology was applied to the two selected case studies, the obtained results demonstrated an appropriate performance of the developed approach, which is evidenced by testing two different leakages configurations. In the WDS representing the background leakages, the obtained results was less than 1% higher than the records obtained by different authors. Meanwhile, in the subsection 8-04 of Bogotá, where leakages were concentrated in certain zones, the results indicate that the valves must be installed where no leakages are present in order to decrease the pressure s surface, reducing the leakages downstream the PRVs.

11 Juan Saldarriaga and Camilo Andrés Salcedo / Procedia Engineering 119 ( 2015 ) Finally, it was demonstrated that the pressure management scheme is an efficient method for reducing leakages in WDS, regarding the use of time-of-day controls where the settings of the PRV are modified along the day according to the demand patterns. References [1] P. Jowitt and C. Xu, Optimal Valve Control in Water Distribution Networks, Journal of Water Resources Planning and Management, vol. 116, no. 4, July/August 1990, pp [2] K. Vairavamoorthy and J. Lumbers, Leakage Reduction in Water Distribution Systems: Optimal Valve Control, Journal of Hydraulic Engineering, vol. 124, no. 11, Nov. 1998, pp [3] E. Creaco and G. Pezzinga, Multiobjective Optimization of Pipe Replacements and Control Valve Installations for Leakage Attenuation in Water Distribution Networks, Journal of Water Resources Planning and Management, /(ASCE)WR , [4] M. E. Ali, Knowledge Based Model for the Optimal Location of Control Valves in Water Distribution Networks, Journal of Water Resources Planning and Management, vol. 141, no. 1, January [5] M. Nicolini and L. Zovatto, Optimal Location and Control of Pressure Reducing Valves in Water Networks, Journal of Water Resources Planning and Management, vol. 135, no. 3, May 2009, pp [6] J. Saldarriaga, S. Ochoa, M. Moreno, N. Romero and O. Cortés, Prioritized Rehabilitation of Water Distribution Networks Using Dissipate Power Concept to Reduce Non-Revenue Water, Urban Water Journal, vol. 7, no. 2, April 2010, pp [7] K. Vairavamoorthy and M. Ali, Pipe Index Vector: A Method to Improve Genetic-Algorithm Based Pipe Optimization, Journal of Hydraulic Engineering, vol. 131, no. 12, December 2005, pp [8] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A Fast and Elitist Multi-objective Genetic Algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, April 2002, pp [9] R. Schulz, A MATLAB Implementation of NSGA-II, a Multi-Objective Genetic Algorithm, 2004, London. [10] K. Deb, Multi-objective Optimization Using Evolutionary Algorithms, John Wiley & Sons Inc, ISBN: , New York, July [11] J. Thornton, Water Loss Control Manual, McGraw Hill ISBN , New York, [12] H. A. Alhimiary and R. H. Alsuhaily, Minimizing Leakage Rates in Water Distribution Networks Through Optimal Valves Settings, Proceedings of World Environmental and Water Resources Congress 2007, pp [13] M. Mahdavi and K. Hosseini, Leakage Control in Water Distribution Networks by Using Optimal Pressure Management: A Case Study, Proceedings of Water Distribution System Analysis 2010, pp [14] L. Rossman, EPANET 2 User s Manual, US Environmental Protection Agency, Cincinnati, Ohio, [15] Water Distribution and Sewer Systems Research Center CIACUA, Plano Óptimo de Presiones Fase II POP II: Informe Final, Universidad de los Andes, Bogotá, 2004.